Abstract
This paper studies the properties of bid and ask prices posted by a monopolistic market maker, without parametric assumptions about the utility function of the market maker or about the probability distribution of the return of the risky asset. We first prove that the two prices can be higher or lower than the expected value of the asset, and that the spread is decreasing in the initial wealth when the market maker exhibits decreasing absolute risk aversion. We conclude by some examples illustrating the fact that almost all shapes can be obtained for the bid–ask spread (as a function of the inventory) depending on the probability distribution of the payment of the risky asset.